Summary
In applications of ensemble-based history matching, it is common to conduct Kalman gain or covariance localization to mitigate spurious correlations and excessive variability reduction resulting from the use of relatively small ensembles. Another alternative strategy not very well explored in reservoir applications is to apply a local analysis scheme, which consists of defining a smaller group of local model variables and observed data (observations), and perform history matching within each group individually. This work aims to demonstrate the practical advantages of a new local analysis scheme over the Kalman gain localization in a 4D seismic history-matching problem that involves big seismic data sets. In the proposed local analysis scheme, we use a correlation-based adaptive data-selection strategy to choose observations for the update of each group of local model variables. Compared to the Kalman gain localization scheme, the proposed local analysis scheme has an improved capacity in handling big models and big data sets, especially in terms of computer memory required to store relevant matrices involved in ensemble-based history-matching algorithms. In addition, we show that despite the need for a higher computational cost to perform model update per iteration step, the proposed local analysis scheme makes the ensemble-based history-matching algorithm converge faster, rendering the same level of data mismatch values at a faster pace. Meanwhile, with the same numbers of iteration steps, the ensemble-based history-matching algorithm equipped with the proposed local analysis scheme tends to yield better qualities for the estimated reservoir models than that with a Kalman gain localization scheme. As such, the proposed adaptive local analysis scheme has the potential of facilitating wider applications of ensemble-based algorithms to practical large-scale history-matching problems.
History matching, also known as data assimilation, is an inverse problem with multiple solutions responsible for generating more reliable models for use in decision-making processes. An iterative ensemble-based method (Ensemble Smoother with Multiple Data Assimilation-ES-MDA) has been used to improve the solution of history-matching processes with a technique called distance-dependent localization. In conjunction, ES-MDA and localization can obtain consistent petrophysical images (permeability and porosity). However, the distance-dependent localization technique is not used to update scalar uncertainties, such as relative permeability; therefore, the variability for these properties is excessively reduced, potentially excluding plausible answers. This work presents three approaches to update scalar parameters while increasing the final variability of these uncertainties to better scan the search space. The three approaches that were developed and compared using a benchmark case are: binary correlation coefficient (BCC), based on correlation calculated by ES-MDA through cross-covariance matrix C f MD (BCC-C MD); BCC, based on a correlation coefficient between the objective functions and scalar uncertainties (R) (BCC-R); and full correlation coefficient (FCC). We used the work of Soares et al. (J Pet Sci Eng 169:110-125, 2018) as a base case to compare the approaches because although it showed good matches with geologically consistent petrophysical images, it generated an excessive reduction in the scalar parameters. BCC-C MD presented similar results to the base case, excessively reducing the variability of the scalar uncertainties. BCC-R increased the variability in the scalar parameters, especially for BCC with a higher threshold value. Finally, FCC found many more potential answers in the search space without impairing data matches and production forecast quality.
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